Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5

Percentage Accurate: 69.5% → 95.3%

Time: 15.2s

Alternatives: 11

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (* 2.0 (sqrt (+ (+ (* x y) (* x z)) (* y z)))))

C

double code(double x, double y, double z) {
	return 2.0 * sqrt((((x * y) + (x * z)) + (y * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 * sqrt((((x * y) + (x * z)) + (y * z)))
end function

Java

public static double code(double x, double y, double z) {
	return 2.0 * Math.sqrt((((x * y) + (x * z)) + (y * z)));
}

Python

def code(x, y, z):
	return 2.0 * math.sqrt((((x * y) + (x * z)) + (y * z)))

Julia

function code(x, y, z)
	return Float64(2.0 * sqrt(Float64(Float64(Float64(x * y) + Float64(x * z)) + Float64(y * z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0 * sqrt((((x * y) + (x * z)) + (y * z)));
end

Wolfram

code[x_, y_, z_] := N[(2.0 * N[Sqrt[N[(N[(N[(x * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 69.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (* 2.0 (sqrt (+ (+ (* x y) (* x z)) (* y z)))))

C

double code(double x, double y, double z) {
	return 2.0 * sqrt((((x * y) + (x * z)) + (y * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 * sqrt((((x * y) + (x * z)) + (y * z)))
end function

Java

public static double code(double x, double y, double z) {
	return 2.0 * Math.sqrt((((x * y) + (x * z)) + (y * z)));
}

Python

def code(x, y, z):
	return 2.0 * math.sqrt((((x * y) + (x * z)) + (y * z)))

Julia

function code(x, y, z)
	return Float64(2.0 * sqrt(Float64(Float64(Float64(x * y) + Float64(x * z)) + Float64(y * z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0 * sqrt((((x * y) + (x * z)) + (y * z)));
end

Wolfram

code[x_, y_, z_] := N[(2.0 * N[Sqrt[N[(N[(N[(x * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 95.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+60}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(y + x\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{\mathsf{fma}\left(\frac{y}{z}, x, y + x\right)} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -3.5e+60)
   (* 2.0 (pow (exp (* 0.25 (- (log (- (- z) y)) (log (/ -1.0 x))))) 2.0))
   (if (<= y 4.6e-277)
     (* 2.0 (sqrt (fma x y (* z (+ y x)))))
     (* 2.0 (* (sqrt (fma (/ y z) x (+ y x))) (sqrt z))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.5e+60) {
		tmp = 2.0 * pow(exp((0.25 * (log((-z - y)) - log((-1.0 / x))))), 2.0);
	} else if (y <= 4.6e-277) {
		tmp = 2.0 * sqrt(fma(x, y, (z * (y + x))));
	} else {
		tmp = 2.0 * (sqrt(fma((y / z), x, (y + x))) * sqrt(z));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -3.5e+60)
		tmp = Float64(2.0 * (exp(Float64(0.25 * Float64(log(Float64(Float64(-z) - y)) - log(Float64(-1.0 / x))))) ^ 2.0));
	elseif (y <= 4.6e-277)
		tmp = Float64(2.0 * sqrt(fma(x, y, Float64(z * Float64(y + x)))));
	else
		tmp = Float64(2.0 * Float64(sqrt(fma(Float64(y / z), x, Float64(y + x))) * sqrt(z)));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -3.5e+60], N[(2.0 * N[Power[N[Exp[N[(0.25 * N[(N[Log[N[((-z) - y), $MachinePrecision]], $MachinePrecision] - N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-277], N[(2.0 * N[Sqrt[N[(x * y + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[N[(N[(y / z), $MachinePrecision] * x + N[(y + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000002e60

   1. Initial program 50.0%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. distribute-lft-out 50.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)} + y \cdot z} \]

      2. *-commutative 50.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y + z\right) \cdot x} + y \cdot z} \]

   4. Applied egg-rr 50.0%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y + z\right) \cdot x} + y \cdot z} \]
   5. Step-by-step derivation

      1. add-sqr-sqrt 49.7%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{\sqrt{\left(y + z\right) \cdot x + y \cdot z}} \cdot \sqrt{\sqrt{\left(y + z\right) \cdot x + y \cdot z}}\right)} \]

      2. pow2 49.7%

         \[\leadsto 2 \cdot \color{blue}{{\left(\sqrt{\sqrt{\left(y + z\right) \cdot x + y \cdot z}}\right)}^{2}} \]

      3. pow1/2 49.7%

         \[\leadsto 2 \cdot {\left(\sqrt{\color{blue}{{\left(\left(y + z\right) \cdot x + y \cdot z\right)}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 49.8%

         \[\leadsto 2 \cdot {\color{blue}{\left({\left(\left(y + z\right) \cdot x + y \cdot z\right)}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. fma-define 50.6%

         \[\leadsto 2 \cdot {\left({\color{blue}{\left(\mathsf{fma}\left(y + z, x, y \cdot z\right)\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2} \]

      6. metadata-eval 50.6%

         \[\leadsto 2 \cdot {\left({\left(\mathsf{fma}\left(y + z, x, y \cdot z\right)\right)}^{\color{blue}{0.25}}\right)}^{2} \]

   6. Applied egg-rr 50.6%

      \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(y + z, x, y \cdot z\right)\right)}^{0.25}\right)}^{2}} \]

   7. Taylor expanded in x around -inf 48.6%

      \[\leadsto 2 \cdot {\color{blue}{\left(e^{0.25 \cdot \left(\log \left(-1 \cdot \left(y + z\right)\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)}\right)}}^{2} \]

   if -3.5000000000000002e60 < y < 4.6e-277

   1. Initial program 86.2%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. +-commutative 86.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. *-commutative 86.2%

         \[\leadsto 2 \cdot \sqrt{\left(x \cdot z + x \cdot y\right) + \color{blue}{z \cdot y}} \]

      3. +-commutative 86.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y + \left(x \cdot z + x \cdot y\right)}} \]

      4. *-commutative 86.2%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(\color{blue}{z \cdot x} + x \cdot y\right)} \]

      5. *-commutative 86.2%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(z \cdot x + \color{blue}{y \cdot x}\right)} \]

      6. associate-+l+ 86.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(z \cdot y + z \cdot x\right) + y \cdot x}} \]

      7. +-commutative 86.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(z \cdot y + z \cdot x\right)}} \]

      8. *-commutative 86.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(z \cdot y + z \cdot x\right)} \]

      9. fma-define 86.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\mathsf{fma}\left(x, y, z \cdot y + z \cdot x\right)}} \]

      10. +-commutative 86.2%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot x + z \cdot y}\right)} \]

      11. distribute-lft-out 86.2%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(x + y\right)}\right)} \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(x + y\right)\right)}} \]
   4. Add Preprocessing

   if 4.6e-277 < y

   1. Initial program 71.4%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. +-commutative 71.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. *-commutative 71.4%

         \[\leadsto 2 \cdot \sqrt{\left(x \cdot z + x \cdot y\right) + \color{blue}{z \cdot y}} \]

      3. +-commutative 71.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y + \left(x \cdot z + x \cdot y\right)}} \]

      4. *-commutative 71.4%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(\color{blue}{z \cdot x} + x \cdot y\right)} \]

      5. *-commutative 71.4%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(z \cdot x + \color{blue}{y \cdot x}\right)} \]

      6. associate-+l+ 71.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(z \cdot y + z \cdot x\right) + y \cdot x}} \]

      7. +-commutative 71.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(z \cdot y + z \cdot x\right)}} \]

      8. *-commutative 71.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(z \cdot y + z \cdot x\right)} \]

      9. fma-define 71.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\mathsf{fma}\left(x, y, z \cdot y + z \cdot x\right)}} \]

      10. +-commutative 71.5%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot x + z \cdot y}\right)} \]

      11. distribute-lft-out 71.6%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(x + y\right)}\right)} \]

   3. Simplified 71.6%

      \[\leadsto \color{blue}{2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(x + y\right)\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 62.5%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(x + \left(y + \frac{x \cdot y}{z}\right)\right)}} \]
   6. Step-by-step derivation

      1. associate-+r+ 62.5%

         \[\leadsto 2 \cdot \sqrt{z \cdot \color{blue}{\left(\left(x + y\right) + \frac{x \cdot y}{z}\right)}} \]

      2. associate-/l* 59.4%

         \[\leadsto 2 \cdot \sqrt{z \cdot \left(\left(x + y\right) + \color{blue}{x \cdot \frac{y}{z}}\right)} \]

   7. Simplified 59.4%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(\left(x + y\right) + x \cdot \frac{y}{z}\right)}} \]
   8. Step-by-step derivation

      1. *-commutative 59.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(\left(x + y\right) + x \cdot \frac{y}{z}\right) \cdot z}} \]

      2. sqrt-prod 54.3%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{\left(x + y\right) + x \cdot \frac{y}{z}} \cdot \sqrt{z}\right)} \]

      3. +-commutative 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\color{blue}{x \cdot \frac{y}{z} + \left(x + y\right)}} \cdot \sqrt{z}\right) \]

      4. clear-num 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{x \cdot \color{blue}{\frac{1}{\frac{z}{y}}} + \left(x + y\right)} \cdot \sqrt{z}\right) \]

      5. *-commutative 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\color{blue}{\frac{1}{\frac{z}{y}} \cdot x} + \left(x + y\right)} \cdot \sqrt{z}\right) \]

      6. fma-define 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\color{blue}{\mathsf{fma}\left(\frac{1}{\frac{z}{y}}, x, x + y\right)}} \cdot \sqrt{z}\right) \]

      7. clear-num 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\mathsf{fma}\left(\color{blue}{\frac{y}{z}}, x, x + y\right)} \cdot \sqrt{z}\right) \]

      8. +-commutative 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\mathsf{fma}\left(\frac{y}{z}, x, \color{blue}{y + x}\right)} \cdot \sqrt{z}\right) \]

   9. Applied egg-rr 54.3%

      \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{\mathsf{fma}\left(\frac{y}{z}, x, y + x\right)} \cdot \sqrt{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+60}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(y + x\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{\mathsf{fma}\left(\frac{y}{z}, x, y + x\right)} \cdot \sqrt{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+61}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(-y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(y + x\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{\mathsf{fma}\left(\frac{y}{z}, x, y + x\right)} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -2.5e+61)
   (* 2.0 (pow (exp (* 0.25 (- (log (- y)) (log (/ -1.0 x))))) 2.0))
   (if (<= y 7.4e-277)
     (* 2.0 (sqrt (fma x y (* z (+ y x)))))
     (* 2.0 (* (sqrt (fma (/ y z) x (+ y x))) (sqrt z))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.5e+61) {
		tmp = 2.0 * pow(exp((0.25 * (log(-y) - log((-1.0 / x))))), 2.0);
	} else if (y <= 7.4e-277) {
		tmp = 2.0 * sqrt(fma(x, y, (z * (y + x))));
	} else {
		tmp = 2.0 * (sqrt(fma((y / z), x, (y + x))) * sqrt(z));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -2.5e+61)
		tmp = Float64(2.0 * (exp(Float64(0.25 * Float64(log(Float64(-y)) - log(Float64(-1.0 / x))))) ^ 2.0));
	elseif (y <= 7.4e-277)
		tmp = Float64(2.0 * sqrt(fma(x, y, Float64(z * Float64(y + x)))));
	else
		tmp = Float64(2.0 * Float64(sqrt(fma(Float64(y / z), x, Float64(y + x))) * sqrt(z)));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -2.5e+61], N[(2.0 * N[Power[N[Exp[N[(0.25 * N[(N[Log[(-y)], $MachinePrecision] - N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.4e-277], N[(2.0 * N[Sqrt[N[(x * y + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[N[(N[(y / z), $MachinePrecision] * x + N[(y + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000009e61

   1. Initial program 50.0%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. associate-+l+ 50.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y + \left(x \cdot z + y \cdot z\right)}} \]

      2. +-commutative 50.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{\left(y \cdot z + x \cdot z\right)}} \]

      3. distribute-rgt-in 50.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 50.0%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 31.6%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y}} \]
   6. Step-by-step derivation

      1. add-sqr-sqrt 31.3%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{\sqrt{x \cdot y}} \cdot \sqrt{\sqrt{x \cdot y}}\right)} \]

      2. pow2 31.3%

         \[\leadsto 2 \cdot \color{blue}{{\left(\sqrt{\sqrt{x \cdot y}}\right)}^{2}} \]

      3. pow1/2 31.9%

         \[\leadsto 2 \cdot {\left(\sqrt{\color{blue}{{\left(x \cdot y\right)}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 32.0%

         \[\leadsto 2 \cdot {\color{blue}{\left({\left(x \cdot y\right)}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. *-commutative 32.0%

         \[\leadsto 2 \cdot {\left({\color{blue}{\left(y \cdot x\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2} \]

      6. metadata-eval 32.0%

         \[\leadsto 2 \cdot {\left({\left(y \cdot x\right)}^{\color{blue}{0.25}}\right)}^{2} \]

   7. Applied egg-rr 32.0%

      \[\leadsto 2 \cdot \color{blue}{{\left({\left(y \cdot x\right)}^{0.25}\right)}^{2}} \]

   8. Taylor expanded in x around -inf 46.7%

      \[\leadsto 2 \cdot {\color{blue}{\left(e^{0.25 \cdot \left(\log \left(-1 \cdot y\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)}\right)}}^{2} \]

   if -2.50000000000000009e61 < y < 7.3999999999999997e-277

   1. Initial program 86.2%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. +-commutative 86.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. *-commutative 86.2%

         \[\leadsto 2 \cdot \sqrt{\left(x \cdot z + x \cdot y\right) + \color{blue}{z \cdot y}} \]

      3. +-commutative 86.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y + \left(x \cdot z + x \cdot y\right)}} \]

      4. *-commutative 86.2%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(\color{blue}{z \cdot x} + x \cdot y\right)} \]

      5. *-commutative 86.2%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(z \cdot x + \color{blue}{y \cdot x}\right)} \]

      6. associate-+l+ 86.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(z \cdot y + z \cdot x\right) + y \cdot x}} \]

      7. +-commutative 86.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(z \cdot y + z \cdot x\right)}} \]

      8. *-commutative 86.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(z \cdot y + z \cdot x\right)} \]

      9. fma-define 86.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\mathsf{fma}\left(x, y, z \cdot y + z \cdot x\right)}} \]

      10. +-commutative 86.2%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot x + z \cdot y}\right)} \]

      11. distribute-lft-out 86.2%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(x + y\right)}\right)} \]

   3. Simplified 86.2%

      \[\leadsto \color{blue}{2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(x + y\right)\right)}} \]
   4. Add Preprocessing

   if 7.3999999999999997e-277 < y

   1. Initial program 71.4%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. +-commutative 71.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. *-commutative 71.4%

         \[\leadsto 2 \cdot \sqrt{\left(x \cdot z + x \cdot y\right) + \color{blue}{z \cdot y}} \]

      3. +-commutative 71.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y + \left(x \cdot z + x \cdot y\right)}} \]

      4. *-commutative 71.4%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(\color{blue}{z \cdot x} + x \cdot y\right)} \]

      5. *-commutative 71.4%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(z \cdot x + \color{blue}{y \cdot x}\right)} \]

      6. associate-+l+ 71.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(z \cdot y + z \cdot x\right) + y \cdot x}} \]

      7. +-commutative 71.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(z \cdot y + z \cdot x\right)}} \]

      8. *-commutative 71.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(z \cdot y + z \cdot x\right)} \]

      9. fma-define 71.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\mathsf{fma}\left(x, y, z \cdot y + z \cdot x\right)}} \]

      10. +-commutative 71.5%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot x + z \cdot y}\right)} \]

      11. distribute-lft-out 71.6%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(x + y\right)}\right)} \]

   3. Simplified 71.6%

      \[\leadsto \color{blue}{2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(x + y\right)\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 62.5%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(x + \left(y + \frac{x \cdot y}{z}\right)\right)}} \]
   6. Step-by-step derivation

      1. associate-+r+ 62.5%

         \[\leadsto 2 \cdot \sqrt{z \cdot \color{blue}{\left(\left(x + y\right) + \frac{x \cdot y}{z}\right)}} \]

      2. associate-/l* 59.4%

         \[\leadsto 2 \cdot \sqrt{z \cdot \left(\left(x + y\right) + \color{blue}{x \cdot \frac{y}{z}}\right)} \]

   7. Simplified 59.4%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(\left(x + y\right) + x \cdot \frac{y}{z}\right)}} \]
   8. Step-by-step derivation

      1. *-commutative 59.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(\left(x + y\right) + x \cdot \frac{y}{z}\right) \cdot z}} \]

      2. sqrt-prod 54.3%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{\left(x + y\right) + x \cdot \frac{y}{z}} \cdot \sqrt{z}\right)} \]

      3. +-commutative 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\color{blue}{x \cdot \frac{y}{z} + \left(x + y\right)}} \cdot \sqrt{z}\right) \]

      4. clear-num 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{x \cdot \color{blue}{\frac{1}{\frac{z}{y}}} + \left(x + y\right)} \cdot \sqrt{z}\right) \]

      5. *-commutative 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\color{blue}{\frac{1}{\frac{z}{y}} \cdot x} + \left(x + y\right)} \cdot \sqrt{z}\right) \]

      6. fma-define 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\color{blue}{\mathsf{fma}\left(\frac{1}{\frac{z}{y}}, x, x + y\right)}} \cdot \sqrt{z}\right) \]

      7. clear-num 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\mathsf{fma}\left(\color{blue}{\frac{y}{z}}, x, x + y\right)} \cdot \sqrt{z}\right) \]

      8. +-commutative 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\mathsf{fma}\left(\frac{y}{z}, x, \color{blue}{y + x}\right)} \cdot \sqrt{z}\right) \]

   9. Applied egg-rr 54.3%

      \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{\mathsf{fma}\left(\frac{y}{z}, x, y + x\right)} \cdot \sqrt{z}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+61}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(-y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(y + x\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{\mathsf{fma}\left(\frac{y}{z}, x, y + x\right)} \cdot \sqrt{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-271}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot \left(z + \left(x + x \cdot \frac{z}{y}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{\mathsf{fma}\left(\frac{y}{z}, x, y + x\right)} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -3.3e-271)
   (* 2.0 (sqrt (* y (+ z (+ x (* x (/ z y)))))))
   (* 2.0 (* (sqrt (fma (/ y z) x (+ y x))) (sqrt z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.3e-271) {
		tmp = 2.0 * sqrt((y * (z + (x + (x * (z / y))))));
	} else {
		tmp = 2.0 * (sqrt(fma((y / z), x, (y + x))) * sqrt(z));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -3.3e-271)
		tmp = Float64(2.0 * sqrt(Float64(y * Float64(z + Float64(x + Float64(x * Float64(z / y)))))));
	else
		tmp = Float64(2.0 * Float64(sqrt(fma(Float64(y / z), x, Float64(y + x))) * sqrt(z)));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -3.3e-271], N[(2.0 * N[Sqrt[N[(y * N[(z + N[(x + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[N[(N[(y / z), $MachinePrecision] * x + N[(y + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3000000000000002e-271

   1. Initial program 72.1%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. +-commutative 72.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. *-commutative 72.1%

         \[\leadsto 2 \cdot \sqrt{\left(x \cdot z + x \cdot y\right) + \color{blue}{z \cdot y}} \]

      3. +-commutative 72.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y + \left(x \cdot z + x \cdot y\right)}} \]

      4. *-commutative 72.1%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(\color{blue}{z \cdot x} + x \cdot y\right)} \]

      5. *-commutative 72.1%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(z \cdot x + \color{blue}{y \cdot x}\right)} \]

      6. associate-+l+ 72.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(z \cdot y + z \cdot x\right) + y \cdot x}} \]

      7. +-commutative 72.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(z \cdot y + z \cdot x\right)}} \]

      8. *-commutative 72.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(z \cdot y + z \cdot x\right)} \]

      9. fma-define 72.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\mathsf{fma}\left(x, y, z \cdot y + z \cdot x\right)}} \]

      10. +-commutative 72.1%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot x + z \cdot y}\right)} \]

      11. distribute-lft-out 72.3%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(x + y\right)}\right)} \]

   3. Simplified 72.3%

      \[\leadsto \color{blue}{2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(x + y\right)\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 69.9%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot \left(x + \left(z + \frac{x \cdot z}{y}\right)\right)}} \]
   6. Step-by-step derivation

      1. +-commutative 69.9%

         \[\leadsto 2 \cdot \sqrt{y \cdot \color{blue}{\left(\left(z + \frac{x \cdot z}{y}\right) + x\right)}} \]

      2. associate-+l+ 69.9%

         \[\leadsto 2 \cdot \sqrt{y \cdot \color{blue}{\left(z + \left(\frac{x \cdot z}{y} + x\right)\right)}} \]

      3. +-commutative 69.9%

         \[\leadsto 2 \cdot \sqrt{y \cdot \left(z + \color{blue}{\left(x + \frac{x \cdot z}{y}\right)}\right)} \]

      4. associate-/l* 65.5%

         \[\leadsto 2 \cdot \sqrt{y \cdot \left(z + \left(x + \color{blue}{x \cdot \frac{z}{y}}\right)\right)} \]

   7. Simplified 65.5%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot \left(z + \left(x + x \cdot \frac{z}{y}\right)\right)}} \]

   if -3.3000000000000002e-271 < y

   1. Initial program 73.1%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. +-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. *-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{\left(x \cdot z + x \cdot y\right) + \color{blue}{z \cdot y}} \]

      3. +-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y + \left(x \cdot z + x \cdot y\right)}} \]

      4. *-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(\color{blue}{z \cdot x} + x \cdot y\right)} \]

      5. *-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(z \cdot x + \color{blue}{y \cdot x}\right)} \]

      6. associate-+l+ 73.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(z \cdot y + z \cdot x\right) + y \cdot x}} \]

      7. +-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(z \cdot y + z \cdot x\right)}} \]

      8. *-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(z \cdot y + z \cdot x\right)} \]

      9. fma-define 73.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\mathsf{fma}\left(x, y, z \cdot y + z \cdot x\right)}} \]

      10. +-commutative 73.2%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot x + z \cdot y}\right)} \]

      11. distribute-lft-out 73.3%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(x + y\right)}\right)} \]

   3. Simplified 73.3%

      \[\leadsto \color{blue}{2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(x + y\right)\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 65.0%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(x + \left(y + \frac{x \cdot y}{z}\right)\right)}} \]
   6. Step-by-step derivation

      1. associate-+r+ 65.0%

         \[\leadsto 2 \cdot \sqrt{z \cdot \color{blue}{\left(\left(x + y\right) + \frac{x \cdot y}{z}\right)}} \]

      2. associate-/l* 62.2%

         \[\leadsto 2 \cdot \sqrt{z \cdot \left(\left(x + y\right) + \color{blue}{x \cdot \frac{y}{z}}\right)} \]

   7. Simplified 62.2%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(\left(x + y\right) + x \cdot \frac{y}{z}\right)}} \]
   8. Step-by-step derivation

      1. *-commutative 62.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(\left(x + y\right) + x \cdot \frac{y}{z}\right) \cdot z}} \]

      2. sqrt-prod 54.3%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{\left(x + y\right) + x \cdot \frac{y}{z}} \cdot \sqrt{z}\right)} \]

      3. +-commutative 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\color{blue}{x \cdot \frac{y}{z} + \left(x + y\right)}} \cdot \sqrt{z}\right) \]

      4. clear-num 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{x \cdot \color{blue}{\frac{1}{\frac{z}{y}}} + \left(x + y\right)} \cdot \sqrt{z}\right) \]

      5. *-commutative 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\color{blue}{\frac{1}{\frac{z}{y}} \cdot x} + \left(x + y\right)} \cdot \sqrt{z}\right) \]

      6. fma-define 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\color{blue}{\mathsf{fma}\left(\frac{1}{\frac{z}{y}}, x, x + y\right)}} \cdot \sqrt{z}\right) \]

      7. clear-num 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\mathsf{fma}\left(\color{blue}{\frac{y}{z}}, x, x + y\right)} \cdot \sqrt{z}\right) \]

      8. +-commutative 54.3%

         \[\leadsto 2 \cdot \left(\sqrt{\mathsf{fma}\left(\frac{y}{z}, x, \color{blue}{y + x}\right)} \cdot \sqrt{z}\right) \]

   9. Applied egg-rr 54.3%

      \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{\mathsf{fma}\left(\frac{y}{z}, x, y + x\right)} \cdot \sqrt{z}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-273}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot \left(z + \left(x + x \cdot \frac{z}{y}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y + x}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -2.85e-273)
   (* 2.0 (sqrt (* y (+ z (+ x (* x (/ z y)))))))
   (* 2.0 (* (sqrt z) (sqrt (+ y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.85e-273) {
		tmp = 2.0 * sqrt((y * (z + (x + (x * (z / y))))));
	} else {
		tmp = 2.0 * (sqrt(z) * sqrt((y + x)));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.85d-273)) then
        tmp = 2.0d0 * sqrt((y * (z + (x + (x * (z / y))))))
    else
        tmp = 2.0d0 * (sqrt(z) * sqrt((y + x)))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.85e-273) {
		tmp = 2.0 * Math.sqrt((y * (z + (x + (x * (z / y))))));
	} else {
		tmp = 2.0 * (Math.sqrt(z) * Math.sqrt((y + x)));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -2.85e-273:
		tmp = 2.0 * math.sqrt((y * (z + (x + (x * (z / y))))))
	else:
		tmp = 2.0 * (math.sqrt(z) * math.sqrt((y + x)))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -2.85e-273)
		tmp = Float64(2.0 * sqrt(Float64(y * Float64(z + Float64(x + Float64(x * Float64(z / y)))))));
	else
		tmp = Float64(2.0 * Float64(sqrt(z) * sqrt(Float64(y + x))));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.85e-273)
		tmp = 2.0 * sqrt((y * (z + (x + (x * (z / y))))));
	else
		tmp = 2.0 * (sqrt(z) * sqrt((y + x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -2.85e-273], N[(2.0 * N[Sqrt[N[(y * N[(z + N[(x + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[z], $MachinePrecision] * N[Sqrt[N[(y + x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.84999999999999986e-273

   1. Initial program 72.1%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. +-commutative 72.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. *-commutative 72.1%

         \[\leadsto 2 \cdot \sqrt{\left(x \cdot z + x \cdot y\right) + \color{blue}{z \cdot y}} \]

      3. +-commutative 72.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y + \left(x \cdot z + x \cdot y\right)}} \]

      4. *-commutative 72.1%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(\color{blue}{z \cdot x} + x \cdot y\right)} \]

      5. *-commutative 72.1%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(z \cdot x + \color{blue}{y \cdot x}\right)} \]

      6. associate-+l+ 72.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(z \cdot y + z \cdot x\right) + y \cdot x}} \]

      7. +-commutative 72.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(z \cdot y + z \cdot x\right)}} \]

      8. *-commutative 72.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(z \cdot y + z \cdot x\right)} \]

      9. fma-define 72.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\mathsf{fma}\left(x, y, z \cdot y + z \cdot x\right)}} \]

      10. +-commutative 72.1%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot x + z \cdot y}\right)} \]

      11. distribute-lft-out 72.3%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(x + y\right)}\right)} \]

   3. Simplified 72.3%

      \[\leadsto \color{blue}{2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(x + y\right)\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 69.9%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot \left(x + \left(z + \frac{x \cdot z}{y}\right)\right)}} \]
   6. Step-by-step derivation

      1. +-commutative 69.9%

         \[\leadsto 2 \cdot \sqrt{y \cdot \color{blue}{\left(\left(z + \frac{x \cdot z}{y}\right) + x\right)}} \]

      2. associate-+l+ 69.9%

         \[\leadsto 2 \cdot \sqrt{y \cdot \color{blue}{\left(z + \left(\frac{x \cdot z}{y} + x\right)\right)}} \]

      3. +-commutative 69.9%

         \[\leadsto 2 \cdot \sqrt{y \cdot \left(z + \color{blue}{\left(x + \frac{x \cdot z}{y}\right)}\right)} \]

      4. associate-/l* 65.5%

         \[\leadsto 2 \cdot \sqrt{y \cdot \left(z + \left(x + \color{blue}{x \cdot \frac{z}{y}}\right)\right)} \]

   7. Simplified 65.5%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot \left(z + \left(x + x \cdot \frac{z}{y}\right)\right)}} \]

   if -2.84999999999999986e-273 < y

   1. Initial program 73.1%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. +-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. *-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{\left(x \cdot z + x \cdot y\right) + \color{blue}{z \cdot y}} \]

      3. +-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y + \left(x \cdot z + x \cdot y\right)}} \]

      4. *-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(\color{blue}{z \cdot x} + x \cdot y\right)} \]

      5. *-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{z \cdot y + \left(z \cdot x + \color{blue}{y \cdot x}\right)} \]

      6. associate-+l+ 73.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(z \cdot y + z \cdot x\right) + y \cdot x}} \]

      7. +-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(z \cdot y + z \cdot x\right)}} \]

      8. *-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(z \cdot y + z \cdot x\right)} \]

      9. fma-define 73.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\mathsf{fma}\left(x, y, z \cdot y + z \cdot x\right)}} \]

      10. +-commutative 73.2%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot x + z \cdot y}\right)} \]

      11. distribute-lft-out 73.3%

          \[\leadsto 2 \cdot \sqrt{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(x + y\right)}\right)} \]

   3. Simplified 73.3%

      \[\leadsto \color{blue}{2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(x + y\right)\right)}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 73.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y + z \cdot \left(x + y\right)}} \]

      2. +-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + z \cdot \color{blue}{\left(y + x\right)}} \]

      3. add-cbrt-cube 53.8%

         \[\leadsto 2 \cdot \color{blue}{\sqrt[3]{\left(\sqrt{x \cdot y + z \cdot \left(y + x\right)} \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}\right) \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}}} \]

      4. pow1/3 50.0%

         \[\leadsto 2 \cdot \color{blue}{{\left(\left(\sqrt{x \cdot y + z \cdot \left(y + x\right)} \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}\right) \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}\right)}^{0.3333333333333333}} \]

   6. Applied egg-rr 50.2%

      \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(x, y, z \cdot \left(x + y\right)\right)\right)}^{1.5}\right)}^{0.3333333333333333}} \]
   7. Step-by-step derivation

      1. unpow1/3 54.0%

         \[\leadsto 2 \cdot \color{blue}{\sqrt[3]{{\left(\mathsf{fma}\left(x, y, z \cdot \left(x + y\right)\right)\right)}^{1.5}}} \]

      2. fma-define 53.8%

         \[\leadsto 2 \cdot \sqrt[3]{{\color{blue}{\left(x \cdot y + z \cdot \left(x + y\right)\right)}}^{1.5}} \]

      3. +-commutative 53.8%

         \[\leadsto 2 \cdot \sqrt[3]{{\color{blue}{\left(z \cdot \left(x + y\right) + x \cdot y\right)}}^{1.5}} \]

      4. fma-define 54.0%

         \[\leadsto 2 \cdot \sqrt[3]{{\color{blue}{\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}}^{1.5}} \]

   8. Simplified 54.0%

      \[\leadsto 2 \cdot \color{blue}{\sqrt[3]{{\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{1.5}}} \]

   9. Taylor expanded in z around inf 35.0%

      \[\leadsto 2 \cdot \sqrt[3]{{\color{blue}{\left(z \cdot \left(x + y\right)\right)}}^{1.5}} \]
   10. Step-by-step derivation

       1. pow1/3 32.7%

          \[\leadsto 2 \cdot \color{blue}{{\left({\left(z \cdot \left(x + y\right)\right)}^{1.5}\right)}^{0.3333333333333333}} \]

       2. pow-pow 47.8%

          \[\leadsto 2 \cdot \color{blue}{{\left(z \cdot \left(x + y\right)\right)}^{\left(1.5 \cdot 0.3333333333333333\right)}} \]

       3. metadata-eval 47.8%

          \[\leadsto 2 \cdot {\left(z \cdot \left(x + y\right)\right)}^{\color{blue}{0.5}} \]

       4. pow1/2 47.8%

          \[\leadsto 2 \cdot \color{blue}{\sqrt{z \cdot \left(x + y\right)}} \]

       5. *-commutative 47.8%

          \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x + y\right) \cdot z}} \]

       6. sqrt-prod 48.8%

          \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{x + y} \cdot \sqrt{z}\right)} \]

       7. +-commutative 48.8%

          \[\leadsto 2 \cdot \left(\sqrt{\color{blue}{y + x}} \cdot \sqrt{z}\right) \]

   11. Applied egg-rr 48.8%

       \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{y + x} \cdot \sqrt{z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-273}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot \left(z + \left(x + x \cdot \frac{z}{y}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y + x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{+29}:\\ \;\;\;\;2 \cdot \sqrt{\left(y + z\right) \cdot x + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 4.2e+29)
   (* 2.0 (sqrt (+ (* (+ y z) x) (* y z))))
   (* 2.0 (* (sqrt z) (sqrt y)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.2e+29) {
		tmp = 2.0 * sqrt((((y + z) * x) + (y * z)));
	} else {
		tmp = 2.0 * (sqrt(z) * sqrt(y));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 4.2d+29) then
        tmp = 2.0d0 * sqrt((((y + z) * x) + (y * z)))
    else
        tmp = 2.0d0 * (sqrt(z) * sqrt(y))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.2e+29) {
		tmp = 2.0 * Math.sqrt((((y + z) * x) + (y * z)));
	} else {
		tmp = 2.0 * (Math.sqrt(z) * Math.sqrt(y));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 4.2e+29:
		tmp = 2.0 * math.sqrt((((y + z) * x) + (y * z)))
	else:
		tmp = 2.0 * (math.sqrt(z) * math.sqrt(y))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 4.2e+29)
		tmp = Float64(2.0 * sqrt(Float64(Float64(Float64(y + z) * x) + Float64(y * z))));
	else
		tmp = Float64(2.0 * Float64(sqrt(z) * sqrt(y)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 4.2e+29)
		tmp = 2.0 * sqrt((((y + z) * x) + (y * z)));
	else
		tmp = 2.0 * (sqrt(z) * sqrt(y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, 4.2e+29], N[(2.0 * N[Sqrt[N[(N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[z], $MachinePrecision] * N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.2000000000000003e29

   1. Initial program 76.6%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. distribute-lft-out 76.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)} + y \cdot z} \]

      2. *-commutative 76.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y + z\right) \cdot x} + y \cdot z} \]

   4. Applied egg-rr 76.6%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y + z\right) \cdot x} + y \cdot z} \]

   if 4.2000000000000003e29 < y

   1. Initial program 58.9%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. associate-+l+ 58.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y + \left(x \cdot z + y \cdot z\right)}} \]

      2. +-commutative 58.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{\left(y \cdot z + x \cdot z\right)}} \]

      3. distribute-rgt-in 58.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 58.9%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 22.2%

      \[\leadsto \color{blue}{2 \cdot \sqrt{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 22.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y}} \]

   7. Simplified 22.2%

      \[\leadsto \color{blue}{2 \cdot \sqrt{z \cdot y}} \]
   8. Step-by-step derivation

      1. sqrt-prod 43.3%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{y}\right)} \]

   9. Applied egg-rr 43.3%

      \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{y}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 69.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-294}:\\ \;\;\;\;2 \cdot \sqrt{\left(y + z\right) \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1e-294) (* 2.0 (sqrt (* (+ y z) x))) (* 2.0 (sqrt (* z (+ y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e-294) {
		tmp = 2.0 * sqrt(((y + z) * x));
	} else {
		tmp = 2.0 * sqrt((z * (y + x)));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1d-294)) then
        tmp = 2.0d0 * sqrt(((y + z) * x))
    else
        tmp = 2.0d0 * sqrt((z * (y + x)))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e-294) {
		tmp = 2.0 * Math.sqrt(((y + z) * x));
	} else {
		tmp = 2.0 * Math.sqrt((z * (y + x)));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1e-294:
		tmp = 2.0 * math.sqrt(((y + z) * x))
	else:
		tmp = 2.0 * math.sqrt((z * (y + x)))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1e-294)
		tmp = Float64(2.0 * sqrt(Float64(Float64(y + z) * x)));
	else
		tmp = Float64(2.0 * sqrt(Float64(z * Float64(y + x))));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1e-294)
		tmp = 2.0 * sqrt(((y + z) * x));
	else
		tmp = 2.0 * sqrt((z * (y + x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -1e-294], N[(2.0 * N[Sqrt[N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000002e-294

   1. Initial program 72.3%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. associate-+l+ 72.3%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y + \left(x \cdot z + y \cdot z\right)}} \]

      2. +-commutative 72.3%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{\left(y \cdot z + x \cdot z\right)}} \]

      3. distribute-rgt-in 72.3%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 72.3%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 48.1%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot \left(y + z\right)}} \]
   6. Step-by-step derivation

      1. +-commutative 48.1%

         \[\leadsto 2 \cdot \sqrt{x \cdot \color{blue}{\left(z + y\right)}} \]

   7. Simplified 48.1%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot \left(z + y\right)}} \]

   if -1.00000000000000002e-294 < y

   1. Initial program 72.9%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. associate-+l+ 72.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y + \left(x \cdot z + y \cdot z\right)}} \]

      2. +-commutative 72.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{\left(y \cdot z + x \cdot z\right)}} \]

      3. distribute-rgt-in 72.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 72.9%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 47.4%

      \[\leadsto \color{blue}{2 \cdot \sqrt{z \cdot \left(x + y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-294}:\\ \;\;\;\;2 \cdot \sqrt{\left(y + z\right) \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-299}:\\ \;\;\;\;2 \cdot \sqrt{\left(y + z\right) \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z \cdot \left(y \cdot 4\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 1.25e-299) (* 2.0 (sqrt (* (+ y z) x))) (sqrt (* z (* y 4.0)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.25e-299) {
		tmp = 2.0 * sqrt(((y + z) * x));
	} else {
		tmp = sqrt((z * (y * 4.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 1.25d-299) then
        tmp = 2.0d0 * sqrt(((y + z) * x))
    else
        tmp = sqrt((z * (y * 4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.25e-299) {
		tmp = 2.0 * Math.sqrt(((y + z) * x));
	} else {
		tmp = Math.sqrt((z * (y * 4.0)));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 1.25e-299:
		tmp = 2.0 * math.sqrt(((y + z) * x))
	else:
		tmp = math.sqrt((z * (y * 4.0)))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 1.25e-299)
		tmp = Float64(2.0 * sqrt(Float64(Float64(y + z) * x)));
	else
		tmp = sqrt(Float64(z * Float64(y * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.25e-299)
		tmp = 2.0 * sqrt(((y + z) * x));
	else
		tmp = sqrt((z * (y * 4.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, 1.25e-299], N[(2.0 * N[Sqrt[N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Sqrt[N[(z * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.24999999999999989e-299

   1. Initial program 73.1%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. associate-+l+ 73.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y + \left(x \cdot z + y \cdot z\right)}} \]

      2. +-commutative 73.1%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{\left(y \cdot z + x \cdot z\right)}} \]

      3. distribute-rgt-in 73.1%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 73.1%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 49.7%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot \left(y + z\right)}} \]
   6. Step-by-step derivation

      1. +-commutative 49.7%

         \[\leadsto 2 \cdot \sqrt{x \cdot \color{blue}{\left(z + y\right)}} \]

   7. Simplified 49.7%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot \left(z + y\right)}} \]

   if 1.24999999999999989e-299 < y

   1. Initial program 72.0%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. associate-+l+ 72.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y + \left(x \cdot z + y \cdot z\right)}} \]

      2. +-commutative 72.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{\left(y \cdot z + x \cdot z\right)}} \]

      3. distribute-rgt-in 72.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 72.0%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 24.1%

      \[\leadsto \color{blue}{2 \cdot \sqrt{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 24.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y}} \]

   7. Simplified 24.1%

      \[\leadsto \color{blue}{2 \cdot \sqrt{z \cdot y}} \]
   8. Step-by-step derivation

      1. add-sqr-sqrt 24.0%

         \[\leadsto \color{blue}{\sqrt{2 \cdot \sqrt{z \cdot y}} \cdot \sqrt{2 \cdot \sqrt{z \cdot y}}} \]

      2. sqrt-unprod 24.1%

         \[\leadsto \color{blue}{\sqrt{\left(2 \cdot \sqrt{z \cdot y}\right) \cdot \left(2 \cdot \sqrt{z \cdot y}\right)}} \]

      3. *-commutative 24.1%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{z \cdot y} \cdot 2\right)} \cdot \left(2 \cdot \sqrt{z \cdot y}\right)} \]

      4. *-commutative 24.1%

         \[\leadsto \sqrt{\left(\sqrt{z \cdot y} \cdot 2\right) \cdot \color{blue}{\left(\sqrt{z \cdot y} \cdot 2\right)}} \]

      5. swap-sqr 24.1%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{z \cdot y} \cdot \sqrt{z \cdot y}\right) \cdot \left(2 \cdot 2\right)}} \]

      6. add-sqr-sqrt 24.1%

         \[\leadsto \sqrt{\color{blue}{\left(z \cdot y\right)} \cdot \left(2 \cdot 2\right)} \]

      7. metadata-eval 24.1%

         \[\leadsto \sqrt{\left(z \cdot y\right) \cdot \color{blue}{4}} \]

   9. Applied egg-rr 24.1%

      \[\leadsto \color{blue}{\sqrt{\left(z \cdot y\right) \cdot 4}} \]
   10. Step-by-step derivation

       1. associate-*l* 24.2%

          \[\leadsto \sqrt{\color{blue}{z \cdot \left(y \cdot 4\right)}} \]

   11. Simplified 24.2%

       \[\leadsto \color{blue}{\sqrt{z \cdot \left(y \cdot 4\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-299}:\\ \;\;\;\;2 \cdot \sqrt{\left(y + z\right) \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z \cdot \left(y \cdot 4\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ 2 \cdot \sqrt{\left(y + z\right) \cdot x + y \cdot z} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* 2.0 (sqrt (+ (* (+ y z) x) (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return 2.0 * sqrt((((y + z) * x) + (y * z)));
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 * sqrt((((y + z) * x) + (y * z)))
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return 2.0 * Math.sqrt((((y + z) * x) + (y * z)));
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return 2.0 * math.sqrt((((y + z) * x) + (y * z)))

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(2.0 * sqrt(Float64(Float64(Float64(y + z) * x) + Float64(y * z))))
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = 2.0 * sqrt((((y + z) * x) + (y * z)));
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(2.0 * N[Sqrt[N[(N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.6%

   \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. distribute-lft-out 72.6%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)} + y \cdot z} \]

   2. *-commutative 72.6%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y + z\right) \cdot x} + y \cdot z} \]

4. Applied egg-rr 72.6%

   \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y + z\right) \cdot x} + y \cdot z} \]
5. Add Preprocessing

Alternative 9: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ 2 \cdot \sqrt{y \cdot x + z \cdot \left(y + x\right)} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* 2.0 (sqrt (+ (* y x) (* z (+ y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return 2.0 * sqrt(((y * x) + (z * (y + x))));
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 * sqrt(((y * x) + (z * (y + x))))
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return 2.0 * Math.sqrt(((y * x) + (z * (y + x))));
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return 2.0 * math.sqrt(((y * x) + (z * (y + x))))

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(2.0 * sqrt(Float64(Float64(y * x) + Float64(z * Float64(y + x)))))
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = 2.0 * sqrt(((y * x) + (z * (y + x))));
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(2.0 * N[Sqrt[N[(N[(y * x), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.6%

   \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
2. Step-by-step derivation

   1. associate-+l+ 72.6%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y + \left(x \cdot z + y \cdot z\right)}} \]

   2. +-commutative 72.6%

      \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{\left(y \cdot z + x \cdot z\right)}} \]

   3. distribute-rgt-in 72.6%

      \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

3. Simplified 72.6%

   \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
4. Add Preprocessing

5. Final simplification 72.6%

   \[\leadsto 2 \cdot \sqrt{y \cdot x + z \cdot \left(y + x\right)} \]
6. Add Preprocessing

Alternative 10: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z \cdot \left(y \cdot 4\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-310) (* 2.0 (sqrt (* y x))) (sqrt (* z (* y 4.0)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-310) {
		tmp = 2.0 * sqrt((y * x));
	} else {
		tmp = sqrt((z * (y * 4.0)));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5d-310)) then
        tmp = 2.0d0 * sqrt((y * x))
    else
        tmp = sqrt((z * (y * 4.0d0)))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-310) {
		tmp = 2.0 * Math.sqrt((y * x));
	} else {
		tmp = Math.sqrt((z * (y * 4.0)));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -5e-310:
		tmp = 2.0 * math.sqrt((y * x))
	else:
		tmp = math.sqrt((z * (y * 4.0)))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-310)
		tmp = Float64(2.0 * sqrt(Float64(y * x)));
	else
		tmp = sqrt(Float64(z * Float64(y * 4.0)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5e-310)
		tmp = 2.0 * sqrt((y * x));
	else
		tmp = sqrt((z * (y * 4.0)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -5e-310], N[(2.0 * N[Sqrt[N[(y * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Sqrt[N[(z * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.999999999999985e-310

   1. Initial program 72.5%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. associate-+l+ 72.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y + \left(x \cdot z + y \cdot z\right)}} \]

      2. +-commutative 72.5%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{\left(y \cdot z + x \cdot z\right)}} \]

      3. distribute-rgt-in 72.5%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 72.5%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 29.1%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y}} \]

   if -4.999999999999985e-310 < y

   1. Initial program 72.7%

      \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
   2. Step-by-step derivation

      1. associate-+l+ 72.7%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y + \left(x \cdot z + y \cdot z\right)}} \]

      2. +-commutative 72.7%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{\left(y \cdot z + x \cdot z\right)}} \]

      3. distribute-rgt-in 72.7%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 72.7%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 23.6%

      \[\leadsto \color{blue}{2 \cdot \sqrt{y \cdot z}} \]
   6. Step-by-step derivation

      1. *-commutative 23.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y}} \]

   7. Simplified 23.6%

      \[\leadsto \color{blue}{2 \cdot \sqrt{z \cdot y}} \]
   8. Step-by-step derivation

      1. add-sqr-sqrt 23.5%

         \[\leadsto \color{blue}{\sqrt{2 \cdot \sqrt{z \cdot y}} \cdot \sqrt{2 \cdot \sqrt{z \cdot y}}} \]

      2. sqrt-unprod 23.6%

         \[\leadsto \color{blue}{\sqrt{\left(2 \cdot \sqrt{z \cdot y}\right) \cdot \left(2 \cdot \sqrt{z \cdot y}\right)}} \]

      3. *-commutative 23.6%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{z \cdot y} \cdot 2\right)} \cdot \left(2 \cdot \sqrt{z \cdot y}\right)} \]

      4. *-commutative 23.6%

         \[\leadsto \sqrt{\left(\sqrt{z \cdot y} \cdot 2\right) \cdot \color{blue}{\left(\sqrt{z \cdot y} \cdot 2\right)}} \]

      5. swap-sqr 23.6%

         \[\leadsto \sqrt{\color{blue}{\left(\sqrt{z \cdot y} \cdot \sqrt{z \cdot y}\right) \cdot \left(2 \cdot 2\right)}} \]

      6. add-sqr-sqrt 23.6%

         \[\leadsto \sqrt{\color{blue}{\left(z \cdot y\right)} \cdot \left(2 \cdot 2\right)} \]

      7. metadata-eval 23.6%

         \[\leadsto \sqrt{\left(z \cdot y\right) \cdot \color{blue}{4}} \]

   9. Applied egg-rr 23.6%

      \[\leadsto \color{blue}{\sqrt{\left(z \cdot y\right) \cdot 4}} \]
   10. Step-by-step derivation

       1. associate-*l* 23.6%

          \[\leadsto \sqrt{\color{blue}{z \cdot \left(y \cdot 4\right)}} \]

   11. Simplified 23.6%

       \[\leadsto \color{blue}{\sqrt{z \cdot \left(y \cdot 4\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z \cdot \left(y \cdot 4\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \sqrt{z \cdot \left(y \cdot 4\right)} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (sqrt (* z (* y 4.0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return sqrt((z * (y * 4.0)));
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = sqrt((z * (y * 4.0d0)))
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return Math.sqrt((z * (y * 4.0)));
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return math.sqrt((z * (y * 4.0)))

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return sqrt(Float64(z * Float64(y * 4.0)))
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = sqrt((z * (y * 4.0)));
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[Sqrt[N[(z * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 72.6%

   \[2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \]
2. Step-by-step derivation

   1. associate-+l+ 72.6%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y + \left(x \cdot z + y \cdot z\right)}} \]

   2. +-commutative 72.6%

      \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{\left(y \cdot z + x \cdot z\right)}} \]

   3. distribute-rgt-in 72.6%

      \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

3. Simplified 72.6%

   \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 25.0%

   \[\leadsto \color{blue}{2 \cdot \sqrt{y \cdot z}} \]
6. Step-by-step derivation

   1. *-commutative 25.0%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y}} \]

7. Simplified 25.0%

   \[\leadsto \color{blue}{2 \cdot \sqrt{z \cdot y}} \]
8. Step-by-step derivation

   1. add-sqr-sqrt 24.8%

      \[\leadsto \color{blue}{\sqrt{2 \cdot \sqrt{z \cdot y}} \cdot \sqrt{2 \cdot \sqrt{z \cdot y}}} \]

   2. sqrt-unprod 25.0%

      \[\leadsto \color{blue}{\sqrt{\left(2 \cdot \sqrt{z \cdot y}\right) \cdot \left(2 \cdot \sqrt{z \cdot y}\right)}} \]

   3. *-commutative 25.0%

      \[\leadsto \sqrt{\color{blue}{\left(\sqrt{z \cdot y} \cdot 2\right)} \cdot \left(2 \cdot \sqrt{z \cdot y}\right)} \]

   4. *-commutative 25.0%

      \[\leadsto \sqrt{\left(\sqrt{z \cdot y} \cdot 2\right) \cdot \color{blue}{\left(\sqrt{z \cdot y} \cdot 2\right)}} \]

   5. swap-sqr 25.0%

      \[\leadsto \sqrt{\color{blue}{\left(\sqrt{z \cdot y} \cdot \sqrt{z \cdot y}\right) \cdot \left(2 \cdot 2\right)}} \]

   6. add-sqr-sqrt 25.0%

      \[\leadsto \sqrt{\color{blue}{\left(z \cdot y\right)} \cdot \left(2 \cdot 2\right)} \]

   7. metadata-eval 25.0%

      \[\leadsto \sqrt{\left(z \cdot y\right) \cdot \color{blue}{4}} \]

9. Applied egg-rr 25.0%

   \[\leadsto \color{blue}{\sqrt{\left(z \cdot y\right) \cdot 4}} \]
10. Step-by-step derivation

    1. associate-*l* 25.0%

       \[\leadsto \sqrt{\color{blue}{z \cdot \left(y \cdot 4\right)}} \]

11. Simplified 25.0%

    \[\leadsto \color{blue}{\sqrt{z \cdot \left(y \cdot 4\right)}} \]
12. Add Preprocessing

Developer Target 1: 82.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\\ \mathbf{if}\;z < 7.636950090573675 \cdot 10^{+176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(t\_0 \cdot t\_0\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (* 0.25 (* (* (pow y -0.75) (* (pow z -0.75) x)) (+ y z)))
          (* (pow z 0.25) (pow y 0.25)))))
   (if (< z 7.636950090573675e+176)
     (* 2.0 (sqrt (+ (* (+ x y) z) (* x y))))
     (* (* t_0 t_0) 2.0))))

C

double code(double x, double y, double z) {
	double t_0 = (0.25 * ((pow(y, -0.75) * (pow(z, -0.75) * x)) * (y + z))) + (pow(z, 0.25) * pow(y, 0.25));
	double tmp;
	if (z < 7.636950090573675e+176) {
		tmp = 2.0 * sqrt((((x + y) * z) + (x * y)));
	} else {
		tmp = (t_0 * t_0) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (0.25d0 * (((y ** (-0.75d0)) * ((z ** (-0.75d0)) * x)) * (y + z))) + ((z ** 0.25d0) * (y ** 0.25d0))
    if (z < 7.636950090573675d+176) then
        tmp = 2.0d0 * sqrt((((x + y) * z) + (x * y)))
    else
        tmp = (t_0 * t_0) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (0.25 * ((Math.pow(y, -0.75) * (Math.pow(z, -0.75) * x)) * (y + z))) + (Math.pow(z, 0.25) * Math.pow(y, 0.25));
	double tmp;
	if (z < 7.636950090573675e+176) {
		tmp = 2.0 * Math.sqrt((((x + y) * z) + (x * y)));
	} else {
		tmp = (t_0 * t_0) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (0.25 * ((math.pow(y, -0.75) * (math.pow(z, -0.75) * x)) * (y + z))) + (math.pow(z, 0.25) * math.pow(y, 0.25))
	tmp = 0
	if z < 7.636950090573675e+176:
		tmp = 2.0 * math.sqrt((((x + y) * z) + (x * y)))
	else:
		tmp = (t_0 * t_0) * 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(0.25 * Float64(Float64((y ^ -0.75) * Float64((z ^ -0.75) * x)) * Float64(y + z))) + Float64((z ^ 0.25) * (y ^ 0.25)))
	tmp = 0.0
	if (z < 7.636950090573675e+176)
		tmp = Float64(2.0 * sqrt(Float64(Float64(Float64(x + y) * z) + Float64(x * y))));
	else
		tmp = Float64(Float64(t_0 * t_0) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (0.25 * (((y ^ -0.75) * ((z ^ -0.75) * x)) * (y + z))) + ((z ^ 0.25) * (y ^ 0.25));
	tmp = 0.0;
	if (z < 7.636950090573675e+176)
		tmp = 2.0 * sqrt((((x + y) * z) + (x * y)));
	else
		tmp = (t_0 * t_0) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.25 * N[(N[(N[Power[y, -0.75], $MachinePrecision] * N[(N[Power[z, -0.75], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Power[z, 0.25], $MachinePrecision] * N[Power[y, 0.25], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, 7.636950090573675e+176], N[(2.0 * N[Sqrt[N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 * t$95$0), $MachinePrecision] * 2.0), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024137 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z 763695009057367500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* 2 (sqrt (+ (* (+ x y) z) (* x y)))) (* (* (+ (* 1/4 (* (* (pow y -3/4) (* (pow z -3/4) x)) (+ y z))) (* (pow z 1/4) (pow y 1/4))) (+ (* 1/4 (* (* (pow y -3/4) (* (pow z -3/4) x)) (+ y z))) (* (pow z 1/4) (pow y 1/4)))) 2)))

  (* 2.0 (sqrt (+ (+ (* x y) (* x z)) (* y z)))))